Volumes of Solids of Revolution / Method of Cylinders

In the previous section we started looking at determine volumes of solids of revolution.  In this section we took cross sections which were rings or disks, found the cross-sectional area & utilized then the following formulas to determine the volume of the solid.

                                   V =∫ _a^bA ( x ) dx           V = ∫_c^d A ( y)  dy

We only utilized cross sections that were in the shape of a disk or a ring.  However, this does not always have to be the case.  We can utilize any shape for the cross sections as long as it can be expanded or contracted to totally cover the solid we're looking at.